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Empire State College
College of St. Rose (Albany, NY) (MEd)
I like to teach starting from where you are and what you know and going to where you want to be and what you want to know. This allows for exploration of many subjects and many ways of learning and experiencing the world. I taught in the public schools for two years. Many students lose interest in school when they are forced to learn things that they have no interest in and can't relate to. The focus on test scores has narrowed down what can be taught and how it can be taught to a point that this problem can no longer be avoided. I learned most of what I know outside the school system myself. I was able to avoid a lot of time and costs in college because I was able to test out of a lot of the coursework. After I left the public schools, I found that the same methods that I used to learn things on my own were helpful in tutoring students who wanted to do better in school, but had found that the schools could not respond to their special needs.
I am very concerned about the state of the public schools at this time. I see little hope that any meaningful reform can be accomplished for a long time yet to come. At the same time there has never been a time when actually knowing thing that are true and can be applied to the world that we live in has been more important. I cannot perform miracles, however I have succeeded with students whom had been abandoned as hopeless by everyone else. Sometimes simply adhering to sound principles of education is all that it takes. I like to teach starting from where you are and what you know and going to where you want to be and what you want to know. This allows for exploration of many subjects and many ways of learning and experiencing the world. I taught in the public schools for two years. Many students lose interest in school when they are forced to learn things that
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Differential equations are those equations that are obtained by taking the derivative of another equation. This is the form of calculus which allows one to calculate the slope of a curve at a single point that is tangent to the curve, given the equation for the curve. It allows one to determine the position, velocity at any given instant, and acceleration of an accelerating object given a single equation describing its position as a function of time and acceleration.
The difficulties of differential calculus lie mostly in the algebra. To actually differentiate requires a knowledge of certain rules and theorems. However the initial equation must first lie in a form that will allow this to be done easily and with meaningful results. This requires a fluid grasp of algebra and a firm grasp of both the concepts and forms by which calculus is accomplished.
I took a calculus course in college which included differential calculus. I got an A in this course. Recently a friend of mine and I have been trying to start a business in alternate energy. We installed a solar hot water heater. The solar heater heated up water in a reservoir. Cold water came into the reservoir through a heat exchanger then went into the regular hot water heater. The water coming off the panels was a lot hotter than we expected. We became concerned that someone might get scalded if water coming out of the tap was too hot. I used math to model the heat flow as water went through two heat exchangers in succession. Then I obtained the first derivative of this equation and set it equal to zero, thus obtaining an equation that would allow us to determine the maximum water temperature coming out of the faucet using data that was easily obtainable by direct measurement. The results that I got using this equation very closely matched the results I got when I actually measured the water temperature.
That is the sum total of all my experience with differential equations. My friend is a mechanical engineer. We have done a lot of projects together, but engineers very seldom actually use calculus in their work. I don't keep calculus in my head like I do with algebra, geometry and trigonometry. I have learned to recognize problems that it might be used for and I have my college textbook to refer to if I ever need it.
I believe I could successfully tutor differential calculus at a first year college level, but that is probably my limit. I could handle multivariate calculus on my own, but I probably wouldn't want to tutor it. I would like to be able to test my equation out on other solar systems, but we haven't had any more solar heating jobs. Currently we are trying to find ways to make those Finnish masonry wood stoves more affordable in the US.
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